# Neural Control and Certificate Repair via Runtime Monitoring

arXiv: https://arxiv.org/abs/2412.12996 · HTML: https://mlsanity.com/paper/2412.12996/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 36 references that are in the map.
- First posted on arXiv 17 Dec 2024.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [A Lyapunov-based Approach to Safe Reinforcement Learning](https://mlsanity.com/paper/1805.07708/) (2018)
- [Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods](https://mlsanity.com/paper/2202.11762/) (2022)
- [Neural Lyapunov Control](https://mlsanity.com/paper/2005.00611/) (2020)
- [Safe Nonlinear Control Using Robust Neural Lyapunov-Barrier Functions](https://mlsanity.com/paper/2109.06697/) (2021)
- [The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systems](https://mlsanity.com/paper/1808.00924/) (2018)
- [Learning Safe Multi-Agent Control with Decentralized Neural Barrier Certificates](https://mlsanity.com/paper/2101.05436/) (2021)
- [Shield Synthesis: Runtime Enforcement for Reactive Systems](https://mlsanity.com/paper/1501.02573/) (2015)
- [An Inductive Synthesis Framework for Verifiable Reinforcement Learning](https://mlsanity.com/paper/1907.07273/) (2019)
- [Stability Verification in Stochastic Control Systems via Neural Network Supermartingales](https://mlsanity.com/paper/2112.09495/) (2021)
- [Adaptive Shielding under Uncertainty](https://mlsanity.com/paper/2010.03842/) (2020)
- [SABLAS: Learning Safe Control for Black-box Dynamical Systems](https://mlsanity.com/paper/2201.01918/) (2022)
- [Some Applications of Polynomial Optimization in Operations Research and Real-Time Decision Making](https://mlsanity.com/paper/1504.06002/) (2015)
- [Runtime-Safety-Guided Policy Repair](https://mlsanity.com/paper/2008.07667/) (2020)
- [Unifying Qualitative and Quantitative Safety Verification of DNN-Controlled Systems](https://mlsanity.com/paper/2404.01769/) (2024)
- [AutoRepair: Automated Repair for AI-Enabled Cyber-Physical Systems under Safety-Critical Conditions](https://mlsanity.com/paper/2304.05617/) (2023)
- [Extent-Compatible Control Barrier Functions](https://mlsanity.com/paper/2001.07210/) (2020)

## Built on by (most cited first, 3 of 3)

- [Formal Verification of Neural Certificates Done Dynamically](https://mlsanity.com/paper/2507.11987/) (2025)
- [Certified Speculative Execution for Untrusted AI Agents](https://mlsanity.com/paper/2606.31023/) (2026)
- [Runtime Monitoring of Supermartingale Certificates](https://mlsanity.com/paper/2610.19701/) (2026)

## Abstract (arXiv)

Learning-based methods provide a promising approach to solving highly non-linear control tasks that are often challenging for classical control methods. To ensure the satisfaction of a safety property, learning-based methods jointly learn a control policy together with a certificate function for the property. Popular examples include barrier functions for safety and Lyapunov functions for asymptotic stability. While there has been significant progress on learning-based control with certificate functions in the white-box setting, where the correctness of the certificate function can be formally verified, there has been little work on ensuring their reliability in the black-box setting where the system dynamics are unknown. In this work, we consider the problems of certifying and repairing neural network control policies and certificate functions in the black-box setting. We propose a novel framework that utilizes runtime monitoring to detect system behaviors that violate the property of interest under some initially trained neural network policy and certificate. These violating behaviors are used to extract new training data, that is used to re-train the neural network policy and the certificate function and to ultimately repair them. We demonstrate the effectiveness of our approach empirically by using it to repair and to boost the safety rate of neural network policies learned by a state-of-the-art method for learning-based control on two autonomous system control tasks.